Circuit for measuring inductance or capacitance



y 22, 1952 J. M. MARZOLF 2,604,511

v CIRCUIT FOR MEASURING INDUCTANCE OR CAPACITANCE Filed March 2, 19 50 VOLTAGE SOURCE SINE WAVE 0 ,Ma 50 mm A M M w E S 0 O ATTORNEYS Patented July 22, 1 952 2,604,511 y r CIRCUIT FOR MEASURING INDUCTANCE on-"icc OR CAPACITANCE Joseph M. Marzolf, Washington, D. C. Application March-'2, 1950,-. SerialNo. 147,312 r iaci ims. 01. its-.183;

(Granted under" the act of March yamcnded Aprilml, 1928; 370 0; G. 757) This invention relates to-a method and appara tus for measuring ther reactive component of; a

complex impedance, and particular toamethod and apparatus for measuringinductance and ca penance.

More particularly this invention relates to a method and apparatus for measuring the inductance or capacitance of a complex-network which includes resistiv components in addition to the reactive components;

This invention also relatesto e. method and apparatus for measuring the voltage drop across only the reactive componentof an impedance which includes both reactive-"and resistive components.

.In the measurement of'inductancein particular and'also certain capacitive loads, the finite resistance associatedwith the indiicti've or capacitiveiinpedan'ce cannot be separated physically from the reactance of the impedance and. cannot oftenibe neglected. This problem exists when it is ne'cessa'ry to measure the voltage/drop across just "the reactive components of'an unknown im-- pedance which includes 'a resis'tive component.

7 One ohfefctjof this invention is therefore to provide'a" simple method-and'apparatus for quickly measuring, the inductance and. capacitance components of an unknown complex impedance.

Another object .of this invention is to providea Simple method" and apparatus. for -quiifl'clyv measuring-the inductance or capacitance of an'unknown complex'n'etwork which} includes an appreciabl resistivecomponent, v

T Still another Object othisinvention is to provide' a simple method and apparatus for quickly measuring only thereactivevolt'age drop'across the reactive componentof an unknown impedance which includes a resistivecomponent.

In the drawings: n Y

Fig. lisa vector diagram illustrating the princi ple's underlying the present method used in measuring the inductance,v capacitance; or voltage drop across the reactivepo'rtionof anunknown impedance. I

Fig. 2 is asimplified' diagrarnvindicating generally one form of apparatuswhich can perform the method ill'ustratedby Fig. L 1

Fig. 3 is a schematic-diagram ofon-e specific form of apparatus used in measuringthe voltage drop. across the reactive component of th unknown impedance.

n One common method or measuringthe inductance or capacitanceof an-unknown impedance which. includes. an-appreciable resistance com ponentis by means or a-Wheatstone bridge; Any-" one who has ever operated such a device knows that in using-such apparatus-the measurement is very'cumbersome since the; bridge must he balanced'by a cut and try method since two quantn ties must be simultaneously varied to achieve a balance. These quantities are the resistive and reactiveiinpedanjce stand'ardsforining the known leg of the bridge;

The presentinvention a .ct j a us equires G fly: the variation of 3 1 sis quantity and consc *ofany capacitance or isgreatly simplified.

In the measuringof thevol-tage dropacross the reactive component of an unknownimpedance which lil'c hid s a? r'eSiS-fii'" 60111150119111 previous apparatusand methods 'required' independent measurement" of voltage, current, and al'so the power consumed; by theimpedance; This obviouslyrequiredthe use of "voltage and current measuring apparatus as well as expensiv power indicatingapparatus,- Even thenjf'urther mathe= matical calculations various independent measurements were taken. 01" course when the voltage drop across thereactive' parts of the impedance is known, ameasure= merit of frequency-and {another calculation would give the value of the indi-icta nceor capacitance.

- The present inventiongreatly simplifies the method and a paratusror'obtaining this reactive voltageand'requires only, a source of excitation providing Y a known current saw through the un-' knownimpedance-a s'ingle voltmeter, and 9, voltage which is equai'tojand degrees out of phase with, th e resistivevoltage-dropacross th uriknown impedance. Thema'gnitudeof the ream tive voltage-is obtainedbyadding"the iatteryoltage to the voltage acrossth'e u-nlrn'own impedance.

Which in efiect' cancels-out the resistive'com' poner it' voltage.

No calculationsar'e'necessary, and no current or power measurements are necessary. The value of the inductance-oi" capacitance is determined directly from a; measurement of this reactiv'evolt a e; and this method enables one to calibrate the voltmeter directly-in units of ca acitanceer'im (instance; for a given voltage source and current now through the unknown impedance; In con trast, deriving the inductance or C from" the prior art voltage measuring previously mentioned is not simply brating' a voltmeter, because wit such prior" methods no voltfiietr'directly reads-the reactive voltage "drop to the Q'XC ll ag'drop but rather a'niather'natieai calculation method wererequired after these capacitance" done b'y'calh- S1 n of the resistive volt and 3, a substantially l is connected to the minals l6l1. The voltage drop across the'impedance 4 may be measured by a conventional voltmeter 5 and. is represented by vector ob. The voltage across the inductive reactanceis repre-. sented by vector ab and the voltage drop across the resistive component of the impedance 4 is represented by vector a which is in'phase with the current vector of. If a voltage 170' is added by generator 13 to the voltage ob across the unknown impedance which is equal to and 180 degrees out of phase with, the voltage drop 0a across the resistive component of the impedance 4, the net voltage 00 will be'equalto the reactive voltage drop ab.'

Since the value of the resistive component of the unknown impedance is not known, there is a problem in obtaining an indication of when voltage bc' is equal to and opposite in phase with resistive voltage 0a or current of). mine if' the voltage component introduced by generator I3 is substantially equal to and opposite in phase with the IR drop through the resistance component of impedance 4 the variation in voltmeter readings indicated by meter 5 must be observed withvariations in the amplitude and the phase of the signal introduced by source l3. To explicate, reference is again made to Fig. 1, where the voltage from source I 3 appearing across terminals [4-45 is represented in magnitude by the length of vectors be" or 120'. If terminal l5 of source 13 is connected to the impedance terminal I! in such a manner that the voltage from source I3 is in time phase with resistive voltage component 0a, then voltmeter 5 will be measuring the magnitude of vector 00'. But, if the voltage from source I3 is in phase opposition with the resistive voltage component 0a, voltmeter 5 will be measuring the magnitude of vector 0c". It is clear from Figure l-that 0c" is smaller in length than vector 00". Now, if the magnitude of vector be", which is the magnitude of the voltage from source 13, is varied until voltmeter 5 reads a minimum, then the voltage measured by voltmeter 5 at-that point is the voltage represented by vector 00', which is equal in magnitude and phase to the reactive voltage drop ab.

The voltage measuring method of this invention has more general application in measuring the actual value or an unknown inductance or capacitance which has appreciable inherent resistance. For this purpose, the voltmeter must be calibrated directly in units of inductance and capacitance. Any one given calibration is only accurate for one current and one frequency However, the range of the meter can be extended by changing the frequency or current used-with any new calibration of the voltmeter. For this application, it is well to use a crystal controlled oscillator for source I which generates a substantially pure sine wave. Also an ammeter 3 is necessary to measure current, and some means, such as variable resistance 2, is required to adjust the current I to the same value regardless of the value of the unknown impedance 4. To improve'the To deter- 10 unknown complex impedance Lby way of. terease of setting ammeter 3, resistance 2 can be some type of constant-current regulator to adjust the current I automatically to some constant pre-selected value. Of course knowing the frequency f, the current I, and the reactive voltage as read on the scale of voltmeter 5, the scale can be calibrated directly in henries or farads from the basic equationswhere I :current .in amps IX -reactive voltage drop in volts #:5314159 ,fzfrequency in cycles L=inductance in henries C=Capacitance in farads a in IX2 V2 L2 where L2 and C2 are respectively the inductance and capacitance readings'for reactive voltages V2 read on voltmeter 5, and V1, is the voltmeter reading when the known inductance or capacitance is measured. v

Thus far, no particular apparatus has been disclosed for source l3 in Figure 3. As previously stated, one requirement for this source is that it must be either in phase, or degrees out of phase, with resistive voltage 0a. Then, by a reversal of terminal connections for the in phase condition, a 180 degree phase relation can be obtained. One way to obtain a voltage in phase with the resistive voltage on is to obtain a voltage which is in phase with the current I since 011 is always in phase with the current I. The voltage across a pure resistance is in phase with the current flowing through it so, in Figure 2, since the same current 'flows through resistance l2 as does through the unknown impedance 4, the voltage across terminals l4 and I5 is in time phase with the voltage drop across the resistive component of impedance 4. Since terminal I5 is already connected to terminal H a phase inversion circuit is necessary to obtain a voltage which is 180 degreesout'of. phase with the resistive voltage 0a. Figure 2 discloses an electron tube as a phase inverter, but it is clear that other phase inversion means can be used as for example a transformer circuit or a Wheatstone bridge circuit. The electron tube means is the preferred embodiment since it is the simplest and most inexpensive means.

As is well known, the voltage between the oathode and plate electrodes of a resistance loaded linear amplifier circuit is 180 degrees out of time phase with the voltage applied between the cathode anad grid electrode. Thus in Figure 2, vacuum tube 6 has'its grid and cathode electrodes respectively connected to terminal I4 and [5 of resistance I 2 which is in series with unknown 5. pe ance 4. amivoltage source. I. Resistance "1 s nected to: plate and direct current power source H connects. between the resistance. ID to cathode 20. The biason tubei is preferably adjusted so that it operates on the linear portion;

of the curve so that,v voltmeter connected between terminals l4 and I6, measures only pure sine wave voltages. Otherwise. an error-in measurement results.- Connected in parallel circuit relation to tube '6 is another substantially pure resistive load circuit comprising capacitance 1 which is a direct current blockingmeans so thatvoltmeter 5 measures only the alternating current voltage across resistance 9, and ,an induct:- ance 8 which nullifies. any phase changing effect of capacitance 1. Of course if resistance 9 is sub-.

to point I4 If the voltmeter scaleis calibrated taking the direct current voltage at plate of tube ,6

into consideration, thencondenser I and inductance8 couldbe omitted altogether and the voltmeter; iconnected directly to the plate circuit of tube 6. p g

It is to be noted that in the-embodiment of Figure 2 andits modifications that when terminal I5 is connected to terminal l1-, the.voltage across terminals and. I5 (or.|4" and l5) is sorelated to the'voltage across impedance l that it will always be in 180 degree phase opposition to the resistive voltage drop in impedancel.

The steps to followin using the apparatus of Figure 2are as follows assuming the meter is calibrated for a known current I1 and a frequency f1: with source l delivering a. sine wave of voltage at frequency f1 resistance 2 is adjusted so that ammeter 3 reads I1 amps; then adjusting potentiometer 9 so that voltmeter 5.readsa minimum, voltmeter 5 will now give the inductance or capacitance ofimpedance; 4.

For some purposes, it may be necessary to measure only relative values of reactance. Such a situation is present in inductance or capacitive liquid level'indicators where only the reactive component of a complex impedance is varied with the, level of" a liquid. Here. the relationship between the liquid level and the reactance change is known, so that by keepingthe'current constant,

the change in voltage reading is proportional to the change in inductive. or capacitive reactance so that the liquid level can also be read directly from the voltmeter reading.

It is to bev noted that this inventionalso has utility'in measuring the resistance of the unknown complex impedance. If a second voltmeter is placed. across terminals M, and I5 in Figure 2 or 3 and the apparatus adjusted to measure the reactance as before explainedsincelthe voltage introduced across these terminals is then equal to the resistive voltage drop-in the unknown complex impedance; knowing the current I will give the .value of the resistance ofthe unknown complex impedance. Of course, this :sec-. ond'voltmeter canbecalibrated directlylin ohms. for any given current 1. Thus with the move- 6iv m'ent of a single control knob. (thatis the knob which varies the magnitude of the voltage across terminals l4 and l5).simultaneous.measurement of both resistance and inductance or. capaci-.' tance of" the unknown complexv impedance is quickly and easily obtained. p

In all the foregoingalaplicationsand circuits it isobvious that the impedance of voltmeter 5 must. be. substantially-greater than the circuit across. whichit is-placed so that ,itwill not have: effect; on .the circuit and" cause measurement' errors. The embodiments thus far disclosed are exemplary only and, except forthe limitations of the claims, variousmodifications. can be madewwithout varying from thexscope of the invention.

The invention described herein may be manu-I factured and usedbyor for theGovernmentxof the United States of America for governmental purposes without the thereon or therefor.

What is claimed is:

- 1;, The. method of. obtaining. the voltagedropi acrossthe reactive component of a complex-unknown impedance which includes a resistive component comprising. the steps of: causing a sine wave of current I to,iflow through said unknown impedance; obtaining a'variablevoltage V across twogiven terminal points. which is'18O degrees out of phase with the current I; connecting oneof the said terminal points to the impedance- Voltage reading on a relativelyhigh resistance voltmeter terminal which will give the. smallest placed between the other terminal pointand the impedance terminal which has not been connected to saidoneuterminal point; varyingflthe magnitude of V" mum, the latter voltage. reading-being the: voltage drop.acrossthereactive component of the impedance.

2. The method of obtaining the voltage drop across thereactive component of a complexunknown impedance which includes a resistive component comprising the steps of: causing a sine Wave of current to flow through the unknown impedance and a resistance'R/ connected: in series circuit relation; obtaining a'v'ol'tage V across two'terminal'points which is degreesout of phase with the voltage across resistance R connecting. one of thesaid terminal points to the impedance terminal which will give the smallest voltage reading V on arelatively high resistance voltmeter placed between the other terminal pointand the impedance terminal which has not been connected to'sai'd one terminal point; varying the magnitude of V so that the reading V is a minimum, the lattcrvoltage reading beingthe voltage drop across the reactive component of the impedance.

- 3. The method of measuring the capacitance orincluctanoe of an unknown complex impedance comprising the steps of: calibrating a voltmeter scale in units-of measure for capacitance and inductance from data of a given current I placed between the other terminal pointand the impedanceterminal which has not been connected to said-one'terminal -poi'n't; varying the payment of any royalties so that the reading V is a minimagnitude ofiV." so that the'reading V is a mini-' quency F; causing a.sine wave of current to' flow through the unknown'impedan'ce and a re-' sistance R connected in series circuit relation;

obtaining a voltage across two terminal points which is 180 degrees out of phase with the voltage across resistance 3; connecting one of said terminal points to the impedance terminal'which will give the smallest voltage reading V on'said voltmeter when it is placed between the other terminal point and the impedanceterminal which has-not been connected to, said one terminal point; varying the magnitude of V so that the reading V is a minimum. f t

5. Apparatus for measuring the inductance or capacitance of an unknown impedance which includes a resistive component comprising the combination of a first pair of connecting terminals across which the unknown impedance is to be placed, a first substantially pure resistance con-' nected to one of said terminals, 'asource of .a sine waveof voltage at a fixed frequency coupled between the other connecting terminal and the unconnected terminal of said first resistance, said source of voltage including a first means for varying the magnitude of current which will flow through the, unknown impedance which will be of a predetermined'magnitude, regardless of the value of said impedance, a second means coupled to saidp'first resistance for developing across a second pair of connectingterminals a voltage which is 180 degrees out of phase with the voltage across said first'resistance, a third means for coupling one of i said second pair of connecting terminals .to one of said firstipairof connecting terminals so that. the voltage developed by said secondmeans will oppose the voltage drop across the resistive component of said unkown impedance, a voltmeter connected between the other terminal of said second pair of connecting terminals and the terminal of said first pair of connecting terminals which has not beenconnected to, said second pair of connecting terminals, a fourth means associated with said second means for adjusting the magnitude of the voltage across saidfsecond pair "of connecting terminals so that, said voltmeter will indicate a minimum voltage, said voltmeter indication being a measure of the reactive impedance of said unknown impedance.

6. Apparatus for measuring the inductance or capacitance of an unknown impedance which in-'' cludes a resistive component comprising the combination of a first pair of connecting terminals across which the unknown impedance is to be placed, a first substantially pure resistance coupled to one of said terminals, a source of a sine wave of voltage at aconstant frequency coupled between the other connecting terminal and the unconnected terminal of said first resistance, said source of voltage including a first means for varying same so that the magnitude of current I which will fiow throughthe unknown impedance will be the same regardless of the value of said impedance, an electron conduction device having an anode, cathode and control electrode, 'a second substantially pure resistance connected to said anode and being 'invseries :circuit relation with a source of direct current voltage and the said cathode electrode, a third substantially pure' resistance-load in parallel circuit relation to said conduction 'devicefsaid cathode coupled to the connecting terminals not connected to said first res1sta'nce,a second means associated with said electron conduction device for adjusting the mag} nitude ofvoltagecoupled from said third resi s t' ance to said voltmeter'so that said voltmeter will indicate a minimum voltage, said voltmeter indi cation being aineasure of the voltage drop across the reactive component of said unknownfim'pedance." 'L Apparat us ior rneasuring the inductance or capacitance of an unknown impedance which includes a resistive component comprising the combination-of a first'pair of connecting terminals across which the unknown impedance is to be placed, a first substantially pureresistance connected to one of said terminals, a source of a sine wave of voltage at a constant frequency coupled between the other connecting terminal and the unconnected terminal of said first resistance, said source of voltage including a first means for varying the magnitude of same sothat the magnitude of current which will'fiow through the unknown impedance will be the same: regardless of the valueof said impedance, an electron conduction device having an anode, cathode and control'electrode, a second substantially pure resistance connected to said anode and being in series circuit relation with'a' sourceof direct current voltage and 'cathodefelectrodes, a third substantially pure resistance load which includes a direct current blocking means in parallel circuit relation, to said conduction device, 'said cathode coupled to the terminal of said first resistance which is coupled to one of said connecting terminals, said control electrode coupled to the other terminal of said first resistance, a'voltmeter coupled between said third'resistance and the one of said first pair of connecting terminals not connected to said first resistance, asecond means associatedwith said electron conduction devicefor adjusting the magnitude of voltage coupledfrom said third resistance to said voltmeter so that saidfvoltmeter will indicate a minimum voltage, said voltmeter indication being a'measure of the voltage dropacross the reactive component of said unknown imped-v ance.

8. The combination ofa first pair of connecting terminals across which an unknown impedance is to be placed, a first substantially pure resistance coupled to one of said terminals, a source of a sine'wave of voltage coupled between the other connecting terminalfand the unconnected terminal of said first resistance, an electron conduction device having an anode, cathode, and control electrode, a second substantially pure resistance connected to said anode and being in a series circuit relation'with a source of direct cur-' rent voltage and the said cathode electrode, said cathode coupled to the terminal of said first resistance which is coupled to one of said connectminal 'ofsaid voltmeter coupled to the one of the:

said first pair of connecting terminals which is not coupled to said first resistance, means associated with said electron conduction device for adjusting the magnitude of voltage coupled to said voltmeter from the plate circuit of said electron conduction device so that voltmeter will indicate a minimum voltage, said minimum voltage being a measure of the value of the voltage drop across the reactive component of said unknown impedance.

9. Apparatus for use in measuring the inductance or capacitance of an unknown impedance which includes a resistive component comprising the combination of a first source of alternating current voltage of stable frequency, a first pair of connecting terminals, across which the unknown impedance is to be placed, coupled to said first source of voltage, a first means coupled to said first pair of connecting terminals for developing across a pair of output connecting terminals a voltage which is 180 degrees out of phase with the current which will flow through said unknown impedance, a second means for coupling one of said output connecting terminals to one of said first pair of connecting terminals so that the.

voltage developed by said first means will oppose the voltage drop across the resistive component of said unknown impedance, a voltmeter connected between the other terminal of said output connecting terminals and the terminal of said first pair of connecting terminals which has not been connected to said output connecting terminals, a third means associated with said second means for adjusting the magnitude of the voltage across said output connecting terminals so that the voltmeter will indicate a minimum voltage, said voltmeter indication being a measure of the reactive impedance of said unknown impedance.

10. Apparatus for use in measuring the inductance or capacitance of an unknown impedance which includes a resistive component comprising the combination of a first source of a1- ternating current voltage of stable frequency,

means coupling said unknown impedance to said source of alternating current voltage to produce a current flow therethrough, a voltmeter connected to measure the voltage drop across said unknown impedance, a second source of alternating current voltage having a phase opposite to the current flow through said unknown impedance coupled to said voltmeter to oppose the resistive voltage drop measured thereby and means for adjusting the amplitude of the voltage from said second source to minimize the reading of said voltmeter, said voltmeter indication being a measure of the reactive impedance of said unknown impedance.

11 Apparatus for use in measuring the inductance or capacitance of an unknown impedance which includes a resistive component comprising the combination of afirst source of alternating current voltage of stable frequency, an

unknown impedance coupled to said first voltage source, a first pair of terminals coupled to said unknown impedance so that the voltage across said terminals is equal in magnitude and phase to the voltage across said unknown impedance, a second pair of terminals, a second source of a1- ternating current voltage connected to said sec- 0nd pair of terminals which develop a voltage across said second pair of terminals which is 180 degrees out of phase with the current which flows through said unknown impedance, means for coupling one of said second pair of terminals to one of said first pair of terminals so that the voltage developed by said second voltage source will oppose the voltage drop across the resistive component of said unknown impedance, a voltage measuring device connected between the other terminal of said second pair of terminals and the terminal of said first pair of terminals which has not been connected to said second pair of terminals, means associated with said second voltage source for adjusting the magnitude of the voltage across said second pair of terminals so that the voltage measuring device will indicate a minimum voltage.

12. The combination comprising a first voltage generating means for developing a sine wave of voltage, a first pair of terminals across which an unknown impedance having resistive and reactive components is to be placed, said first means being in series circuit relation with said first pair of terminals, a voltmeter and a second voltage generating means coupled across said first pair of terminals, said second voltage generating means generating a voltage which is opposite in phase to the voltage developed across one of the impedance components of said unknown impedance, means coupled to one of said voltage generating means for adjusting the amplitude of the output of same to a value giving a minimum indication on said voltmeter whereby the voltage indicated thereby is a measure of the other impedance component of said unknown impedance.

13. Apparatus for use in measuring the capacitance or inductance of an unknown complex impedance comprising a series circuit comprising an alternating current voltage source of substantially constant current characteristic, first and second terminals to which the unknown impedance is adapted to be coupled, a second circuit parallel to said unknown impedance for applying thereacross a voltage opposite in phase to that supplied by said source, said second circuit comprising a variable potential sampling means having at least a pair of terminals, one terminal of which is connected to one side of said unknown impedance, and a high resistance voltmeter seriall connected between the other terminal of said potential sampling means and the other side of said unknown impedance.

JOSEPH M. MARZOLF.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 1,931,460 Lilienfeld Oct. 17, 1933 2,273,066 Povey Feb. 17, 1942 2,329,098 Browning et a1. Sept. 7, 1943 2,557,798 Reitz, Jr. June 19, 1951 FOREIGN PATENTS Number Country Date 451,094 Great Britain July 29, 1936 

